The following relates generally to wireless communication, and more specifically to orthogonal modulation of signals using maximal length sequences (m-sequences) and Hadamard transforms. Wireless communications systems are widely deployed to provide various types of communication content such as voice, video, packet data, messaging, broadcast, and so on. These systems may be multiple-access systems capable of supporting communication with multiple users by sharing the available system resources (e.g., time, frequency, and power). Examples of such multiple-access systems include code-division multiple access (CDMA) systems, time-division multiple access (TDMA) systems, frequency-division multiple access (FDMA) systems, and orthogonal frequency-division multiple access (OFDMA) systems. The following description may be used in conjunction with one of these technologies, or it may be used in a new system. A wireless system using these techniques may be referred to as orthogonal sequence division multiple access (OSDMA).
Generally, a wireless multiple-access communications system may include a number of base stations, each simultaneously supporting communication for multiple mobile devices. Base stations may communicate with mobile devices on downstream and upstream links. Each base station has a coverage range, which may be referred to as the coverage area of the cell. In some cases, a base station may transmit data to more than one mobile device at a time. A base station may also receive data from more than one mobile device. This may result in interference between communications with the different mobile devices. Interference may also arise when transmissions take more than one path to a receiver. Multipath propagation may result in a delayed and/or distorted version of a signal interfering with the signal that arrives via the most direct path. Communication between a base station and a mobile device may be one directional (e.g., broadcasting information from a base station to a mobile device) or two-directional (e.g., transmitting information back and forth between a base station and a mobile device).
In some cases, data may be processed so that different communication channels or different devices use orthogonal resources to reduce interference. The amount of processing power required may depend on the method used to transform the signal. For example, OFDMA systems apply a Fourier transform to create signals using orthogonal frequency resources. A fast Fourier transform (FFT) processor may perform on the order of N·log N multiplication operations to transform a modulation symbol consisting of N elements. A cyclic prefix may be appended to the signal to reduce inter-symbol interference (ISI) due to multipath propagation. Alternatively, a fast Hadamard transform (FHT) may be used to generate a signal consisting of orthogonal sequences. An FHT processor may transform a signal of size N using on the order of N·log N addition or subtraction operations, which may be more efficient than using multiplication operations. However, using an FHT produces a signal that may not be compatible with the use of a cyclic prefix, and may not have desirable cross-correlation and auto-correlation properties.